1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
|
/*
* Copyright 2010-2011 INRIA Saclay
* Copyright 2012 Ecole Normale Superieure
*
* Use of this software is governed by the MIT license
*
* Written by Sven Verdoolaege, INRIA Saclay - Ile-de-France,
* Parc Club Orsay Universite, ZAC des vignes, 4 rue Jacques Monod,
* 91893 Orsay, France
* and Ecole Normale Superieure, 45 rue d’Ulm, 75230 Paris, France
*/
#include <stdlib.h>
#include <isl/ctx.h>
#include <isl_tarjan.h>
void isl_tarjan_graph_free(struct isl_tarjan_graph *g)
{
if (!g)
return;
free(g->node);
free(g->stack);
free(g->order);
free(g);
}
static struct isl_tarjan_graph *isl_tarjan_graph_alloc(isl_ctx *ctx, int len)
{
struct isl_tarjan_graph *g;
int i;
g = isl_calloc_type(ctx, struct isl_tarjan_graph);
if (!g)
return NULL;
g->len = len;
g->node = isl_alloc_array(ctx, struct isl_tarjan_node, len);
if (len && !g->node)
goto error;
for (i = 0; i < len; ++i)
g->node[i].index = -1;
g->stack = isl_alloc_array(ctx, int, len);
if (len && !g->stack)
goto error;
g->order = isl_alloc_array(ctx, int, 2 * len);
if (len && !g->order)
goto error;
g->sp = 0;
g->index = 0;
g->op = 0;
return g;
error:
isl_tarjan_graph_free(g);
return NULL;
}
/* Perform Tarjan's algorithm for computing the strongly connected components
* in the graph with g->len nodes and with edges defined by "follows".
*/
static int isl_tarjan_components(struct isl_tarjan_graph *g, int i,
int (*follows)(int i, int j, void *user), void *user)
{
int j;
g->node[i].index = g->index;
g->node[i].min_index = g->index;
g->node[i].on_stack = 1;
g->index++;
g->stack[g->sp++] = i;
for (j = g->len - 1; j >= 0; --j) {
int f;
if (j == i)
continue;
if (g->node[j].index >= 0 &&
(!g->node[j].on_stack ||
g->node[j].index > g->node[i].min_index))
continue;
f = follows(i, j, user);
if (f < 0)
return -1;
if (!f)
continue;
if (g->node[j].index < 0) {
isl_tarjan_components(g, j, follows, user);
if (g->node[j].min_index < g->node[i].min_index)
g->node[i].min_index = g->node[j].min_index;
} else if (g->node[j].index < g->node[i].min_index)
g->node[i].min_index = g->node[j].index;
}
if (g->node[i].index != g->node[i].min_index)
return 0;
do {
j = g->stack[--g->sp];
g->node[j].on_stack = 0;
g->order[g->op++] = j;
} while (j != i);
g->order[g->op++] = -1;
return 0;
}
/* Decompose the graph with "len" nodes and edges defined by "follows"
* into strongly connected components (SCCs).
* follows(i, j, user) should return 1 if "i" follows "j" and 0 otherwise.
* It should return -1 on error.
*
* If SCC a contains a node i that follows a node j in another SCC b
* (i.e., follows(i, j, user) returns 1), then SCC a will appear after SCC b
* in the result.
*/
struct isl_tarjan_graph *isl_tarjan_graph_init(isl_ctx *ctx, int len,
int (*follows)(int i, int j, void *user), void *user)
{
int i;
struct isl_tarjan_graph *g = NULL;
g = isl_tarjan_graph_alloc(ctx, len);
if (!g)
return NULL;
for (i = len - 1; i >= 0; --i) {
if (g->node[i].index >= 0)
continue;
if (isl_tarjan_components(g, i, follows, user) < 0)
goto error;
}
return g;
error:
isl_tarjan_graph_free(g);
return NULL;
}
|
